Human subjects localized brief 1/6‐oct bandpassed noise bursts that were centered at 6, 8, 10, and 12 kHz. All testing was done under binaural conditions. The horizontal component of subjects’ responses was accurate, comparable to that for broadband localization, but the vertical and front/back components exhibited systematic errors. Specifically, responses tended to cluster within restricted ranges that were specific for each center frequency. The directional transfer functions of the subjects’ external ears were measured for 360 horizontal and vertical locations. The spectra of the sounds that were present in the subjects’ ear canals, the ‘‘proximal stimulus’’ spectra, were computed by combining the spectra of the narrow‐band sound sources with the directional transfer functions for particular stimulus locations. Subjects consistently localized sounds to regions within which the associated directional transfer function correlated most closely with the proximal stimulus spectrum. A quantitative model was constructed that successfully predicted subjects’ responses based on interaural level difference and spectral cues. A test of the model, using techniques adapted from signal detection theory, indicated that subjects tend to use interaural level difference and spectral shape cues independently, limited only by a slight spatial correlation of the two cues. A testing procedure is described that provides a quantitative comparison of various predictive models of sound localization.

Narrow‐band sound localization related to external ear acoustics

In this tutorial, head-related transfer functions (HRTFs) are introduced and treated with respect to their role in the synthesis of spatial sound over headphones. HRTFs are formally defined, and are shown to be important in reducing the ambiguity with which the classical duplex theory decodes a free-field sound's spatial location. Typical HRTF measurement strategies are described, and simple applications of HRTFs to headphone-based spatialized sound synthesis are given. By comparing and contrasting representations of HRTFs in the time, frequency, and spatial domains, different analytic and signal processing techniques used to investigate the structure of HRTFs are highlighted.

Introduction to Head-Related Transfer Functions (HRTFs): Representations of HRTFs in Time, Frequency, and Space

This study examined inter-subject differences in the transfer functions from the free field to the human ear canal, which are commonly know as head-related transfer functions. The directional components of such transfer functions are referred here to as directional transfer functions (DTFs). The DTFs of 45 subjects varied systematically among subjects in regard to the frequencies of spectral features such as peaks and notches. Inter-subject spectral differences in DTFs were quantified between 3.7 and 12.9 kHz for sound-source directions throughout the coordinate sphere. For each pair of subjects, an optimal frequency scale factor aligned spectral features between subjects and, thus, minimized inter-subject spectral differences. Frequency scaling of DTFs reduced spectral differences by a median value of 15.5% across all pairs of subjects and by more than half in 9.5% of subject pairs. Optimal scale factors showed a median value of 1.061 and a maximum of 1.38. The optimal scale factor between any pair of subjects correlated highly with the ratios of subjects’ maximum interaural delays, sizes of their external ears, and widths of their heads.

Individual differences in external-ear transfer functions reduced by scaling in frequency.

Head-related transfer functions (HRTFs) for human subjects in anechoic space were modeled with modified phase spectra, including minimum-phase-plus-delay, linear-phase, and reversed-phase-plus-delay functions. The overall (wide-band) interaural time delay (ITD) for the modeled HRTFs was made consistent with that of the empirical HRTFs by setting the position-dependent, frequency-independent delay in the HRTF for the lagging ear. Signal analysis of the minimum-phase-plus-delay reconstructions indicated that model HRTFs deviate from empirical HRTF measurements maximally for contralateral azimuths and low elevations. Subjects assessed the perceptual validity of the model HRTFs in a four-interval, two-alternative, forced-choice discrimination paradigm. Results indicate that monaural discrimination performance of subjects was at chance for all three types of HRTF models. Binaural discrimination performance was at chance for the linear-phase HRTFs, was above chance for some locations for the minimum-phase-plus-delay HRTFs, and was above chance for all tested locations for the reversed-phase-plus-delay HRTFs. An analysis of low-frequency timing information showed that all of these results are consistent with efficient use of interaural time differences in the low-frequency components of the stimulus waveforms. It is concluded that listeners are insensitive to HRTF phase spectra as long as the overall ITD of the low-frequency components does not provide a reliable cue. In particular, the minimum-phase-plus-delay approximation to the HRTF phase spectrum is an adequate approximation as long as the low-frequency ITD is appropriate. These results and conclusions are all limited to the anechoic case when the HRTFs correspond to brief impulse responses limited to a few milliseconds.

Sensitivity of human subjects to head-related transfer-function phase spectra

In everyday listening, sound reaches our ears directly from a source as well as indirectly via reflections known as reverberation. Reverberation profoundly distorts the sound from a source, yet humans can both identify sound sources and distinguish environments from the resulting sound, via mechanisms that remain unclear. The core computational challenge is that the acoustic signatures of the source and environment are combined in a single signal received by the ear. Here we ask whether our recognition of sound sources and spaces reflects an ability to separate their effects and whether any such separation is enabled by statistical regularities of real-world reverberation. To first determine whether such statistical regularities exist, we measured impulse responses (IRs) of 271 spaces sampled from the distribution encountered by humans during daily life. The sampled spaces were diverse, but their IRs were tightly constrained, exhibiting exponential decay at frequency-dependent rates: Mid frequencies reverberated longest whereas higher and lower frequencies decayed more rapidly, presumably due to absorptive properties of materials and air. To test whether humans leverage these regularities, we manipulated IR decay characteristics in simulated reverberant audio. Listeners could discriminate sound sources and environments from these signals, but their abilities degraded when reverberation characteristics deviated from those of real-world environments. Subjectively, atypical IRs were mistaken for sound sources. The results suggest the brain separates sound into contributions from the source and the environment, constrained by a prior on natural reverberation. This separation process may contribute to robust recognition while providing information about spaces around us.

https://www.pnas.org/content/pnas/early/2016/11/09/1612524113.full.pdf

Statistics of natural reverberation enable perceptual separation of sound and space

This paper describes a digital processing technique for measuring the impulse response of a system. The method utilizes "complementary" codes as described by Golay in 1961 and has been employed by designers of radar, communications and other equipment. This paper discusses the implementation of the technique in a device that measures the impulse response of audio bandwidth systems. The paper begins by describing the general problem of impulse response measurement using digital methods. This leads to a "unit pulse" response sequence that completely characterizes a bandlimited, linear and time-invariant system. Next, Schroeder's (1979) method of probing the system with pseudo-random noise and correlating the result to obtain an estimate of this response is discussed. Our method is a variation on this scheme wherein the system is probed twice using sequences chosen from among the Golay codes. These codes have the remarkable property that their autocorrelation functions have complementary side-lobes. Finally, the response of a speaker/microphone pair is measured using the proposed method.

S. Foster

Papers

Impulse response measurement using Golay codes